An inference rule is a logical structure that permits deriving conclusions from premises. It specifies the valid steps in reasoning,…
An indirect proof, also known as proof by contradiction, involves assuming the opposite of what you want to prove. If…
A higher-order quantifier binds variables that range over properties, relations, or functions, rather than individuals. This allows for more expressive…
Higher-order logic extends first-order logic by enabling quantification over predicates and other higher-order entities. It offers greater expressive power for…
A formal proof is a rigorous demonstration of truth within a formal system. Each step is precisely justified by a…
A first-order theory formalizes mathematical reasoning using first-order logic. It defines relationships between individuals, properties, and relations, forming the foundation…
The deduction theorem states that if a statement can be derived from a set of premises plus an additional statement,…
A theory with a decision procedure, allowing algorithmic determination of truth or falsehood for any statement within its framework. This…
A constructive proof shows a mathematical object exists by providing a method to build it. This contrasts with indirect proofs,…
The absorption law states that if P implies Q, then adding a conjunction R to P does not alter the…